Is it safe to mix operating systems? ...Does AC run on 64 bit?
Yes, AC will run fine.
I have a mixed network of PCs: 32bit Win XP Pro, 32bit Win Vista Business, 64bit Win7 Pro and 64bit WinServer 2008/R2, with AC running well on each machine. You do not need to use the Win XP mode on Windows 7 to run AC.
Make sure you have the Pro or better level of Windows XP or 7. The Home versions do not network well.
Your main problem with introducing a 64bit computer on your network may be finding drivers for your peripherals, if you use network printers or a network fax. Some older peripherals haven't been updated.